The short answer is not really.
The "compression factor" (hardness/softness) of a ball helps determine how much surface area of the ball makes contact with the clubface at impact, and also how long the ball stays on the clubface before launching. The contact area is generally more important in the overall game; the more of the ball that "squishes" against the clubface, the more the clubhead can induce backspin. Backspin creates lift to keep the ball in the air, but decreases rolling distance. So, more backspin (and thus a softer ball) is usually good for iron shots, and a double-edged sword for drivers; the ball carries further, rolls less.
The amount of time the ball spends in contact with the clubface also helps determine backspin, but more importantly it determines the total impulse (force applied over time) applied to the ball. The speed and mass of the clubhead, thus its available energy, are constant; what changes is how long the ball is receiving energy from the clubhead. This used to be a big deal; you were supposed to match compression factor to your clubhead speed and driver clubhead mass, in order to get a combination that fully "loaded" the ball without overcompressing it (which would waste the energy, damage the ball, and could cause shots to "balloon" due to too much backspin). However, modern drivers incorporate head designs that flex on contact, and provide a similar "trampoline effect" that you used to want out of the ball itself. These new drivers make compression factor less important; with the same driver, a "high compression" and "low compression" ball may only produce 4-5 yards difference in distance given the exact same swing.
Temperature can also be a factor; as the temperature drops, a ball with a low compression factor behaves like a ball with a higher compression factor does in warmer weather. So, you may use a softer ball in November than you would normally use in July to get the same basic behavior.
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